We develop the deformation theory of $A_{infty}$ algebras together with $infty$-inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, $A_{infty}$ algebras, associative algebras with inner products, and $A_{infty}$ algebras with inner products.
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机译：我们开发了$ A _ { infty} $代数与$ infty $内积的变形理论，并确定了控制该理论的微分渐变李代数。这概括了关联代数，$ A _ { infty} $代数，具有内积的关联代数和具有内部积的$ A _ { infty} $代数的变形理论。
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